CAMELOT FANTASIES

Lady TT, it stands for: Officer of the Most Excellent Order of the British Empire.

It is a post-nominal title and an honour to receive this and become a member in the order of chivalry of Great Britain.
It is usually awarded due to outstanding service in battle, high visible accomplishments in one's profession, significant acts of charity, and so on.

Only the top two orders of chivalry are automatically permitted to use the 'Sir' or 'Dame' title before their name.
Knight Grand Cross or Dame Grand Cross of the Most Excellent Order of the British Empire (GBE)
Knight Commander or Dame Commander of the Most Excellent Order of the British Empire (KBE or DBE)

But one may be knighted without attaining those titles. 

Mr. Murray, OBE, could still be promoted or knighted later on and become Sir Andrew Murray.

Respectfully,
masterclass